In three-dimensional (3-d) geological modeling of subterranean hydrocarbon reservoirs, the connected geocellulars or geobodies are of particular interest for reservoir production and performance analysis. For example, where the hydrocarbon deposits are located, where they will flow and what flow rates are possible in different parts of the reservoir could be important for planning where wells should be sunk into the reservoir and how fast the hydrocarbon should be pumped from each well without creating e.g. cavitation problems.
A 3-d geological reservoir model essentially comprises a large number of volume cells (commonly in excess of one million), each associated with a number of physical parameters or seismic attributes. Physical parameters may include for example porosity and permeability; seismic attributes may include e.g. impedance. For some cells of the model the parameters will have been measured directly and for others they will be estimated values. Geobody calculation involves searching the cells of the model, determining based on seismic attributes and/or physical parameters which cells form part of a productive region of the reservoir and then labeling those productive cells which are connected together to make a geobody. Put another way, it can be thought of as the identification of a connected group of cells which are sufficiently capable of supporting hydrocarbon flow that they can be considered together to be a single “pocket” of hydrocarbon deposit.
Various techniques have been described or developed in the past for establishing the geobodies in a reservoir model. The so called “cluster multiple labeling technique” is described in J. Hoshen & R. Kopelman: “Percolation and cluster distribution. I Cluster multiple labeling technique and critical concentration algorithm,” Physical Review B, 14 (1976) p. 3438. In this reference, a percolation based algorithm assigns multiple labels to the same cluster found by bonds with a limited neighborhood radius, then removes the redundant labels to obtain a unique label for each cluster. Multiple labeling and removal of redundant labeling make this algorithm costly in terms of central processing unit (CPU) time for a large geological model.
In the article Clayton V. Deutsch: “Fortran programs for calculating connectivity of three dimensional numerical models and for ranking multiple realizations,” Computers & Geosciences, 24 (1998) p. 69 an algorithm is described which scans the binary indicator values (flags) in a 3 dimensional grid of volume cells in a geological model. The X-stack, Y-stack, and Z-stack are separately and sequentially scanned to locate connected cells and geobody codings applied to connected cells. Duplicated geobody codings are inevitably created, which are removed in subsequent scans. Again, multiple visits to each volume cell and redundant application of geobody identifiers mean that this algorithm would be costly in CPU time for a large geological model. This algorithm is embodied in a program known as geo_obj (“geo-objects”)
In U.S. Pat. No. 5,757,663 (Lo and Chu), two methods are proposed to calculate the geobodies connected to well perforated zones. The first is the directional search (also known as the “pacman” method) which propagates from each well-perforated cell and finds all its connected neighbors in a certain direction until there is no further connected neighbor in that direction and then changes to another direction at the last stop location. The second is an iterative search which acts in a similar way to the Deutsch method (see reference above) but once the scan reaches grid boundaries it sweeps the property again in the opposite direction; this process repeats until all X, Y and Z directions are fully scanned. The method uses the well perforation locations as starting points; for this reason, it cannot find those isolated geobodies which are not connected to the current wells. This method also involves repeated visits to each cell, which makes it costly in CPU time.
In practical analysis of hydrocarbon reservoirs, where there are many unknowns, it is normal to work with a large number of alternative realizations of a reservoir model all of which represent possible configurations of the various reservoir parameters. Geobody analysis is needed for each realization. Statistics such as the distribution of geobody size, the reservoir geobody connectivity and reservoir-well connectivity may be calculated for the purpose of ranking the realizations. It is highly desirable to be able to perform geobody analysis without taking up excessive computing resource, to allow analysis of multiple realizations in a realistic time frame using conventional computer hardware.
Commonly used software for calculating geobody information includes the program “geo_obj” (see the Deutsch reference above) and the Petrel® utility function, marketed by Schlumberger Limited. For a one million cell model, using face connection only, the “geo_obj” program takes 82 seconds on an IBM® T40 laptop (1.3 GHz processor and 768 Mbytes of memory). Using the 2008 version of the Petrel® software, the same process takes 46 seconds. For a 50 million cell model using face connection, both “geo_obj” and Petrel® 2008 failed, even using a Dell® desktop computer with 3 GHz processors and 3 GBytes of memory.